- #1
Klaus_Hoffmann
- 86
- 1
After studying Cesaro and Borel summation i think that
sum [tex] \sum_{p} p^{k} [/tex] extended over all primes is summable Cesaro [tex] C(n,k+1+\epsilon) [/tex]
and the series [tex] \sum_{n=0}^{\infty} M(n) [/tex] and [tex] \sum_{n=0}^{\infty} \Psi (n)-n [/tex]
are Cesaro-summable [tex] C(n,3/2+\epsilon) [/tex] for any positive epsilon
hence the fact that M(0)+M(1)+M(2)+... is Cearo summable 3/2+e is a consequence of Riemann Hypothesis.
sum [tex] \sum_{p} p^{k} [/tex] extended over all primes is summable Cesaro [tex] C(n,k+1+\epsilon) [/tex]
and the series [tex] \sum_{n=0}^{\infty} M(n) [/tex] and [tex] \sum_{n=0}^{\infty} \Psi (n)-n [/tex]
are Cesaro-summable [tex] C(n,3/2+\epsilon) [/tex] for any positive epsilon
hence the fact that M(0)+M(1)+M(2)+... is Cearo summable 3/2+e is a consequence of Riemann Hypothesis.
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